S tochki zreniya klassicheskoy teorii differentsial"nykh uravneniy sistemy differentsial"nykh uravneniy, soderzhashchie proizvedenie obobshchennykh funktsiy yavlyayutsya nekorrektnymi, v svyazi s etim voznikaet neobkhodimost" korrektnogo opredeleniya ukazannogo tipa sistem, poskol"ku poluchaemoe reshenie sushchestvenno zavisit ot ispol"zuemogo sposoba opredeleniya proizvedeniya. V nastoyashchee vremya odno iz napravleniy issledovaniya differentsial"nykh uravneniy s obobshchennymi koeffitsientami predpolagaet ikh izuchenie v ramkakh teorii algebr novykh obobshchennykh funktsiy ili mnemofunktsiy. Dannaya kniga posvyashchena issledovaniyu zadachi Koshi dlya sistem differentsial"nykh uravneniy s obobshchennymi koeffitsientami i sistem differentsial"nykh vklyucheniy s obobshchennoy pravoy chast"yu v pryamom proizvedenii algebr mnemofunktsiy. V knige provoditsya klassifikatsiya assotsiirovannykh resheniy ukazannykh sistem v pryamom proizvedenii algebr mnemofunktsiy v sluchayakh kogda pravaya chast" soderzhit proizvedenie lipshitsevykh funktsiy i obobshchennykh proizvodnykh funktsiy ogranichennoy variatsii, razryvnykh funktsiy i obobshchennykh proizvodnykh nepreryvnykh funktsiy ogranichennoy variatsii, razryvnykh funktsiy i obobshchennykh proizvodnykh kusochno-postoyannykh funktsiy.